Simplify the following expression: $a = \dfrac{k^2 + 9k + 14}{k + 7} $
First factor the polynomial in the numerator. $ k^2 + 9k + 14 = (k + 7)(k + 2) $ So we can rewrite the expression as: $a = \dfrac{(k + 7)(k + 2)}{k + 7} $ We can divide the numerator and denominator by $(k + 7)$ on condition that $k \neq -7$ Therefore $a = k + 2; k \neq -7$